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What is the equivalent resistance between a and b in given figure

What is the equivalent resistance between a and b in given figure

Question Image
Grade:12

1 Answers

Samyak Jain
333 Points
2 years ago
Clearly, 15 \Omega and 10 \Omega resistors are in series since same current flows through them.
Similarly, 20 \Omega and 30 \Omega are in series and 40 \Omega 10 \Omega are in series.
Equivalent series resistance of 15 \Omega and 10 \Omega is (15 + 10) = 25 \Omega, that of 20 \Omega and 30 \Omega is 50 \Omega
and that of 40 \Omega and 10 \Omega is 50 \Omega.
Take a point D between 2 \Omega and 5 \Omega whose potential is VD. Since the potential across a connecting wire
is same, potential of a point between 40 \Omega and 30 \Omega is also VD. Now, take a point C between two 10 \Omega resistors
whose potential is VC, which is also the potential of a point between 8 \Omega and 20 \Omega.
In short, potential difference between equivalent series resistance of 15 \Omega and 10 \Omega (25 \Omega), between
equivalent series resistance of 40 \Omega and 10 \Omega (50 \Omega) and between equivalent series resistance of
20 \Omega and 30 \Omega (50 \Omega) is same and is |VC – VD| i.e.
25 \Omega, 50 \Omega and 50 \Omega resistors are in parallel whose equivalent resistance is
1/(1/25 + 1/50 + 1/50) \Omega =  1/{(2 + 1 + 1)/50} \Omega =  50 / 4 \Omega = 25/2 \Omega.
This 25/2 \Omega resistance is in series with 2 \Omega and 8 \Omega resistors.
\therefore The equivalent resistance between points A and B is (25/2 + 2 + 8) \Omega = 45/2 \Omega.

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